A106641 A four-symbol four-at-a-time substitution with an ordering change: q=0.

1, 2, 2, 1, 4, 1, 1, 4, 4, 1, 1, 4, 1, 2, 2, 1, 2, 3, 3, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 3, 3, 2, 2, 3, 3, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 3, 3, 2, 1, 2, 2, 1, 4, 1, 1, 4, 4, 1, 1, 4, 1, 2, 2, 1, 4, 1, 1, 4, 3, 4, 4, 3, 3, 4, 4, 3, 4, 1, 1, 4, 1, 2, 2, 1, 4, 1, 1, 4, 4, 1, 1, 4, 1, 2, 2, 1, 1, 2, 2, 1, 4, 1, 1, 4, 4

Offset

0,2

Comments

This substitution gives two border-like 90-degree fractals, one (q=0) of which appears to tile.

Links

Table of n, a(n) for n=0..104.

Formula

1->{3, 4, 4, 3}, 2->q*{3, 2, 2, 3} + (1 - q)*{2, 3, 3, 2}, 3->{1, 2, 2, 1}, 4->q*{1, 4, 4, 1} + (1 - q)*{4, 1, 1, 4}.

Mathematica

q = 0; s[1] = {3, 4, 4, 3}; s[2] = q*{3, 2, 2, 3} + (1 -q)*{2, 3, 3, 2}; s[3] = {1, 2, 2, 1}; s[4] = q*{1, 4, 4, 1} + (1 - q)*{4, 1, 1, 4}; t[a_] := Flatten[s /@ a] p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] aa = p[4]

Crossrefs

Sequence in context: A214722 A071430 A092514 * A191785 A320500 A140957

Adjacent sequences: A106638 A106639 A106640 * A106642 A106643 A106644

Keyword

nonn,uned

Author

Roger L. Bagula, May 12 2005

Status

approved